I've had good results when I followed these steps:

• Bring the code into a revision control system.
• Build test data and a test sytem so that proper operation can be verified with an automated test.
• Create an independent test environment, do not change production code.
• Fix the worst parts of the code, using test data to make sure that the new system gets the same results as the old system.

You will almost certainly find bugs and want to fix them. Use a boss-approved release process and give users warning that the system is changing.

Get users to test the improvements before release.

If you can't develop a realistic test system, you will have to work much harder and develop many test cases that verify that you aren't changing anything. With this increase in level of difficulty, it might not be justifiable to recode the system.